A) \[{{x}^{2}}/a+x/b+1/c=0\]
B) \[c{{x}^{2}}+bx+a=0\]
C) \[b{{x}^{2}}+cx+a=0\]
D) \[a{{x}^{2}}+cx+b=0\]
Correct Answer: B
Solution :
Given \[\alpha ,\beta \] are the roots of the equation \[a{{x}^{2}}+bx+c=0.\] \[\therefore \] \[\alpha +\beta =-\frac{b}{a}\] and \[\alpha \beta =\frac{c}{a}\] Sum of the given roots \[=\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }\] \[=-\frac{b}{a}\times \frac{a}{c}=-\frac{b}{c}\] and product of the given roots \[=\frac{1}{\alpha }.\frac{1}{\beta }=\frac{a}{c}\] \[\therefore \] Required equations is \[{{x}^{2}}-\] (sum of roots) \[x+\] product of roots = 0 \[\Rightarrow \] \[{{x}^{2}}+\frac{b}{c}x+\frac{a}{c}=0\] \[\Rightarrow \] \[c{{x}^{2}}+bx+a=0\]
You need to login to perform this action.
You will be redirected in
3 sec
